\select@language {spanish}
\contentsline {section}{\numberline {1}Resumen}{4}{section.1}
\contentsline {section}{\numberline {2}Jerarqu\IeC {\'\i }a de Archivos e Instrucciones de Compilado}{5}{section.2}
\contentsline {section}{\numberline {3}Introducci\IeC {\'o}n Te\IeC {\'o}rica}{7}{section.3}
\contentsline {subsection}{\numberline {3.1}Sistemas de equaciones lieneales}{7}{subsection.3.1}
\contentsline {subsection}{\numberline {3.2}Tipos de sistemas}{7}{subsection.3.2}
\contentsline {subsection}{\numberline {3.3}Resoluci\IeC {\'o}n de sistemas}{8}{subsection.3.3}
\contentsline {subsubsection}{\numberline {3.3.1}Inestabilidad num\'erica al usar el algoritmo de Gauss}{8}{subsubsection.3.3.1}
\contentsline {subsection}{\numberline {3.4}Armado de sistema equivalente con eliminaci\IeC {\'o}n de Gauss-Jordan }{8}{subsection.3.4}
\contentsline {subsection}{\numberline {3.5}Matriz traspuesta}{9}{subsection.3.5}
\contentsline {subsection}{\numberline {3.6}Multiplicaci\IeC {\'o}n entre matrices}{9}{subsection.3.6}
\contentsline {section}{\numberline {4}Desarrollo}{10}{section.4}
\contentsline {subsection}{\numberline {4.1}Calibraci\IeC {\'o}n}{10}{subsection.4.1}
\contentsline {subsubsection}{\numberline {4.1.1}Parseo de la Esfera}{10}{subsubsection.4.1.1}
\contentsline {subsubsection}{\numberline {4.1.2}Centrar la esfera y obtener radio}{10}{subsubsection.4.1.2}
\contentsline {subsubsection}{\numberline {4.1.3}Obtenci\IeC {\'o}n del punto de mayor iluminaci\IeC {\'o}n}{11}{subsubsection.4.1.3}
\contentsline {subsubsection}{\numberline {4.1.4}Obtenci\IeC {\'o}n del vector de iluminaci\IeC {\'o}n}{11}{subsubsection.4.1.4}
\contentsline {subsection}{\numberline {4.2}Campo Normal}{12}{subsection.4.2}
\contentsline {subsubsection}{\numberline {4.2.1}Parseo y recorte de im\IeC {\'a}genes}{12}{subsubsection.4.2.1}
\contentsline {subsubsection}{\numberline {4.2.2}Construcci\IeC {\'o}n del campo normal}{12}{subsubsection.4.2.2}
\contentsline {subsection}{\numberline {4.3}Hallar la profundidad}{13}{subsection.4.3}
\contentsline {subsubsection}{\numberline {4.3.1}Obtenci\IeC {\'o}n del sistema $M x = v$}{13}{subsubsection.4.3.1}
\contentsline {subsubsection}{\numberline {4.3.2}Implementaci\IeC {\'o}n de la matriz esparsa}{14}{subsubsection.4.3.2}
\contentsline {subsubsection}{\numberline {4.3.3}Multiplicaci\IeC {\'o}n $M^t$ por $M$}{16}{subsubsection.4.3.3}
\contentsline {subsubsection}{\numberline {4.3.4}Multiplicaci\IeC {\'o}n de $M^t$ por $v$}{17}{subsubsection.4.3.4}
\contentsline {subsubsection}{\numberline {4.3.5}Triangulaci\IeC {\'o}n del sistema $M^t M * x = M^t v$}{17}{subsubsection.4.3.5}
\contentsline {subsubsection}{\numberline {4.3.6}Despeje de inc\IeC {\'o}gnitas}{18}{subsubsection.4.3.6}
\contentsline {section}{\numberline {5}Resultados}{20}{section.5}
\contentsline {subsection}{\numberline {5.1}Campos Normales}{20}{subsection.5.1}
\contentsline {subsubsection}{\numberline {5.1.1}Esfera}{20}{subsubsection.5.1.1}
\contentsline {subsection}{\numberline {5.2}Representaciones en 3D}{23}{subsection.5.2}
\contentsline {subsubsection}{\numberline {5.2.1}Esfera}{23}{subsubsection.5.2.1}
\contentsline {section}{\numberline {6}Discusi\IeC {\'o}n}{24}{section.6}
\contentsline {subsection}{\numberline {6.1}Acerca de los resultados}{24}{subsection.6.1}
\contentsline {subsection}{\numberline {6.2}Imperfecciones}{24}{subsection.6.2}
\contentsline {subsection}{\numberline {6.3}Dificultades}{25}{subsection.6.3}
\contentsline {section}{\numberline {7}Conclusiones}{26}{section.7}
\contentsline {section}{\numberline {8}Ap\IeC {\'e}ndices}{27}{section.8}
\contentsline {subsection}{\numberline {8.1}A - Enunciado}{27}{subsection.8.1}
\contentsline {subsection}{\numberline {8.2}B - C\IeC {\'o}digo Fuente}{27}{subsection.8.2}
\contentsline {section}{\numberline {9}Referencias}{28}{section.9}
